A BOHR PHENOMENON FOR ELLIPTIC EQUATIONS

In 1914 Bohr proved that there is an $r \in (0,1)$ such that if a power series converges in the unit disk and its sum has modulus less than $1$ then, for $|z| < r$, the sum of absolute values of its terms is again less than $1$. Recently, analogous results have been obtained for functions of seve...

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Bibliographic Details
Published inProceedings of the London Mathematical Society Vol. 82; no. 2; pp. 385 - 401
Main Authors AIZENBERG, LEV, TARKHANOV, NIKOLAI
Format Journal Article
LanguageEnglish
Published Cambridge University Press 01.03.2001
Oxford University Press
Subjects
elliptic equation
harmonic function
Harnack inequality
series expansion
Harnack inequality
harmonic function
series expansion
elliptic equation
Online AccessGet full text
ISSN0024-6115
1460-244X
DOI10.1112/S0024611501012813

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Summary:In 1914 Bohr proved that there is an $r \in (0,1)$ such that if a power series converges in the unit disk and its sum has modulus less than $1$ then, for $|z| < r$, the sum of absolute values of its terms is again less than $1$. Recently, analogous results have been obtained for functions of several variables. The aim of this paper is to place the theorem of Bohr in the context of solutions to second-order elliptic equations satisfying the maximum principle. 2000 Mathematics Subject Classification: 35J15, 32A05, 46A35.
Bibliography:ark:/67375/HXZ-MS1NJW3N-R
ArticleID:82.2.385
istex:7808B30EC4D645672641F256841856E2A43416E0
ISSN:0024-6115
1460-244X
DOI:10.1112/S0024611501012813